Problem: Rewrite as a simplified fraction. ${1.7\overline{93} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1793.9393...\\ 10x &= 17.9393...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1776}$ ${x = \dfrac{1776}{990}} $ ${x = \dfrac{296}{165}} \text{or} {1 \dfrac{131}{165}}$